one 
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top). For our example imagery, the recording of this strip of 
ca. 2100 m ground distance took about 20 s. 
All 10 spectral bands of both raw images have been registered 
to a map of scale 1:25 000. First, a simple scanner specific 
panorama correction was applied which accounts for the fact 
that within each scan line the ground coordinate of the ob- 
served pixel varies with the tangens of the scan angle. Then, 
ground control points between raw image and digitized map 
were fixed by eye appraisal for both recordings. We specified 
17 GCPs for 1991 and 33 GCPs for 1995. The same GCP 
sets were used for all experiments. 
We have implemented six different coordinate transforma- 
tions to perform ground control point registration: 
» Global second degree polynomial transformation 
(Richards, 1993). 
P Bivariate AKIMA interpolation: after Delauney trian- 
gulation between the GCPs, quintic polynomials are 
fitted locally, forming a piecewisely defined but smooth 
interpolation (Akima, 1978, Wiemker, 1996). 
P Elastic registration with an affine part and the thin- 
plate spline radial basis function U(r) = r?In r (Book- 
stein, 1989). 
» Registration with an affine part and the radial basis 
function U(r) =r. 
» Pure multiquadric registration with HARDY's radial ba- 
sis function U(r) = v/1 + r2 (Hardy, 1971). 
» Multiquadric registration with a prior global sec- 
ond degree polynomial transformation and subsequent 
HARDY's radial basis function U(r) = V1 + r2. 
All these interpolation techniques are used independently for 
xz and y in order to establish the proper coordinate trans- 
formation functions as determined by the given GCPs. The 
resampling of the image reflectance values was done following 
a nearest neighbor scheme which is strongly recommended for 
multispectral data sets (Richards, 1993). 
The schemes as listed above have been applied for image-to- 
map registration for the imagery of both years 1991 and 1995 
(Fig: 2). 
4. CHANGE DETECTION BY PRINCIPAL 
COMPONENT ANALYSIS 
Following a common concept in remote sensing, change de- 
tection can be conducted for each spectral band by regression 
of the reflectances measured at different recording times, in 
our example 7, = 1991 and T» — 1995, for each pixel in 
the registered images (see Fig. 1). Each pixel then produces 
a point in the two dimensional feature space spanned by the 
two axes of reflectance for T; and T5. Ideally, with no change 
present in the scene, all these reflectance pairs should be on 
the diagonal idendity-axis. Due to potential radiometric cal- 
ibration errors (such as misjudged irradiance and path radi- 
ance), the unchanged points might not be on the diagonal 
axis, but still they will be scattered on an axis given by a linear 
relation between the reflectance values. This 'no change'-axis 
can be found as the first component of a principal compo- 
nent analysis (Richards, 1993). Any remaining variance in 
951 
  
  
    
  
  
Change Detection by Principal Component Analysis in Feature Space 
reflectance at T9 
1.PC 
€ h , 
D change 
reflectance at T 1 
  
  
  
Figure 1: Change detection between overlaying pixels from 
different years by principal component analysis for each spec- 
tral band: areas of 'changed' and 'unchanged' pixels in the 
feature space. 
the direction of the second component is consequently con- 
sidered as 'change'. Thus the second eigenvalue of the 2 x 2 
regression covariance matrix denotes the amount of change 
between the two images taken of the same scene. 
Such detected 'change' is of course prone to errors of the 
prior registration. The 'change' is a superposition of 'real 
change' in the ground truth and erroneous change produced 
by the registration. The quality of the registration is thus 
crucial to pixelwise change detection. For real imagery we 
do not know the amount of 'real change'. However, we can 
utilize the amount of overall 'change' for evaluation of the 
registration quality, since improved registration reduces the 
amount of pseudo-change, with the amount of 'real change' 
as a lower bound. 
5. EXPERIMENTAL RESULTS 
For each of the above named registration techniques, the 
map-registered images of 1991 and 1995 were overlayed for 
each spectral band (for illustration, Fig. 3 shows the over- 
lay for band 6). The difference between global polynomial 
registration and a locally adaptive one such as e.g. AKIMA 
is pronounced and illustrated by the coordinate displacement 
image in Fig. 4. The difference between the locally adap- 
tive methods, however, is not detectable by eye appraisal of 
the overall image, and has to be evaluated by means of the 
principal component change detection. 
The overlaying pixels were identified and a regression in fea- 
ture space was performed. The apparent amount of 'change', 
i.e. the second covariance eigenvalue, decreases with qualita- 
tively better registration which reduces the number of mis- 
registered pixels. The results are tabulated in Table 1. The 
‘change’-reduction is given in percent relative to the conven- 
tional global second degree polynomial transformation. The 
results show that the amount of erroneous change is signif- 
icantly reduced by local AKIMA registration and even more 
by the radial basis function techniques, up to 13.5% in single 
spectral bands. The mean reductions of the various methods 
indicate that already the local AKIMA registration is clearly 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996